Jeongho Ahn, Kenneth L. Kuttler, Meir Shillor
Abstract:
The dynamic contact of two nonlinear Gao beams that are connected
with a joint is modeled, analyzed, and numerically simulated.
Contact is modeled with either (i) the normal compliance condition, or
(ii) the unilateral Signorini condition. The model is in the form
of a variational equality in case (i) and a variational
inequality in case (ii). The existence of the unique variational solution
is established for the problem with normal compliance and the existence
of a weak solution is proved in case (ii).
The solution in the second case is obtained as a limit
of the solutions of the first case when the normal compliance stiffness
tends to infinity. A numerical algorithm for the problem is constructed
using finite elements and a mixed time discretization.
Simulation results, based on the implementation of the algorithm,
of the two cases when the horizontal traction
vanishes or when it is sufficiently large to cause buckling, are presented.
The spectrum of the vibrations, using the FFT, shows a rather noisy system.
Submitted June 7, 2012. Published November 6, 2012.
Math Subject Classifications: 74M15, 35L86,74K10, 74M15, 35L70.
Key Words: Dynamic contact; Gao beam; mechanical joint; normal compliance;
Signorini condition; weak solutions; numerical scheme
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Jeongho Ahn Department of Mathematics and Statistics Arkansas State University State University, AR 72467, USA email: jahn@astate.edu |
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Kenneth L. Kuttler Department of Mathematics Brigham Young University, Provo, UT 84602, USA email: klkuttle@math.byu.edu |
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Meir Shillor Department of Mathematics and Statistics Oakland University Rochester, MI 48309, USA email: shillor@oakland.edu |
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